Question

Missy is constructing a fence that consists of parallel sides line AB and line EF. Complete the proof to explain how she can show that m∠AKL = 116° by filling in the missing justifications. Statement Justification line AB ∥ line EF m∠KLF = 116° Given m∠KLF+ m∠BKL = 180° 1. m∠BKL + m∠AKL = 180° Linear Pair Postulate m∠KLF + m∠BKL = m∠BKL + m∠AKL 2. m∠KLF = m∠AKL Subtraction Property m∠AKL = m∠KLF Symmetric Property m∠AKL = 116° Substitution Property A. 1. Alternate Interior Angles Theorem; 2. Substitution Property B. 1. Definition of Complementary Angles; 2. Substitution Property C. 1. Definition of Supplementary Angles; 2. Transitive Property D. 1. Same-Side Interior Angles Theorem; 2. Transitive Property

Answer 1

Answer:

The correct option is;

D. 1. Same-Side Interior Angles Theorem

2. Transitive Property

Step-by-step explanation:

The two column proof is given as follows;

Statement    ${}$                                            Justification

line AB║line EF   ${}$                                       Given

m∠KLF = 116°    ${}$                                          Given

1. m∠KLF + m∠BKL = 180    ${}$                      1. Same side supplementary angles

2. m∠BKL + m∠AKL = 180°    ${}$                     Linear pair postulate

3. m∠KLF + m∠BKL = m∠BKL + m∠AKL    ${}$2. Transitive property

4. m∠KLF = m∠AKL   ${}$                                  Subtraction property      

5. m∠AKL = m∠KLF  ${}$                                   Symmetric property

6. m∠AKL = 116°  ${}$                                         Substitution property.